Time-dependent Internal DFT formalism and Kohn-Sham scheme

We generalize to the time-dependent case the stationary Internal DFT / Kohn-Sham formalism presented in Ref. [14]. We prove that, in the time-dependent case, the internal properties of a self-bound system (as an atomic nuclei) are all defined by the internal one-body density and the initial state. We set-up a time-dependent Internal Kohn-Sham scheme as a practical way to compute the internal density. The main difference with the traditional DFT / Kohn-Sham formalism is the inclusion of the center-of-mass correlations in the functional.Comment: 13 pages. To be published in Phys. Rev.

Traffic jams induced by rare switching events in two-lane transport

We investigate a model for driven exclusion processes where internal states are assigned to the particles. The latter account for diverse situations, ranging from spin states in spintronics to parallel lanes in intracellular or vehicular traffic. Introducing a coupling between the internal states by allowing particles to switch from one to another induces an intriguing polarization phenomenon. In a mesoscopic scaling, a rich stationary regime for the density profiles is discovered, with localized domain walls in the density profile of one of the internal states being feasible. We derive the shape of the density profiles as well as resulting phase diagrams analytically by a mean-field approximation and a continuum limit. Continuous as well as discontinuous lines of phase transition emerge, their intersections induce multi-critical behaviour

Internal wave pressure, velocity, and energy flux from density perturbations

Determination of energy transport is crucial for understanding the energy budget and fluid circulation in density varying fluids such as the ocean and the atmosphere. However, it is rarely possible to determine the energy flux field $\mathbf{J} = p \mathbf{u}$, which requires simultaneous measurements of the pressure and velocity perturbation fields, $p$ and $\mathbf{u}$. We present a method for obtaining the instantaneous $\mathbf{J}(x,z,t)$ from density perturbations alone: a Green's function-based calculation yields $p$, and $\mathbf{u}$ is obtained by integrating the continuity equation and the incompressibility condition. We validate our method with results from Navier-Stokes simulations: the Green's function method is applied to the density perturbation field from the simulations, and the result for $\mathbf{J}$ is found to agree typically to within $1\%$ with $\mathbf{J}$ computed directly using $p$ and $\mathbf{u}$ from the Navier-Stokes simulation. We also apply the Green's function method to density perturbation data from laboratory schlieren measurements of internal waves in a stratified fluid, and the result for $\mathbf{J}$ agrees to within $6\%$ with results from Navier-Stokes simulations. Our method for determining the instantaneous velocity, pressure, and energy flux fields applies to any system described by a linear approximation of the density perturbation field, e.g., to small amplitude lee waves and propagating vertical modes. The method can be applied using our Matlab graphical user interface EnergyFlux

Self-Similar Solutions of Triaxial Dark Matter Halos

We investigate the collapse and internal structure of dark matter halos. We consider halo formation from initially scale-free perturbations, for which gravitational collapse is self-similar. Fillmore and Goldreich (1984) and Bertschinger (1985) solved the one dimensional (i.e. spherically symmetric) case. We generalize their results by formulating the three dimensional self-similar equations. We solve the equations numerically and analyze the similarity solutions in detail, focusing on the internal density profiles of the collapsed halos. By decomposing the total density into subprofiles of particles that collapse coevally, we identify two effects as the main determinants of the internal density structure of halos: adiabatic contraction and the shape of a subprofile shortly after collapse; the latter largely reflects the triaxiality of the subprofile. We develop a simple model that describes the results of our 3D simulations. In a companion paper, we apply this model to more realistic cosmological fluctuations, and thereby explain the origin of the nearly universal (NFW-like) density profiles found in N-body simulations.Comment: corresponds to version published in Ap

Local density dependent potential for compressible mesoparticles

We focus on finding a coarse grained description able to reproduce the thermodynamic behavior of a molecular system by using mesoparticles representing several molecules. Interactions between mesoparticles are modelled by an interparticle potential, and an additional internal equation of state is used to account for the thermic contribution of coarse grained internal degrees of freedom. Moreover, as strong non-equilibrium situations over a wide range of pressure and density are targeted, the internal compressibility of these mesoparticles has to be considered. This is done by introducing a dependence of the potential on the local environment of the mesoparticles, either by defining a spherical local density or by means of a Voronoi tessellation. As an example, a local density dependent potential is fitted to reproduce the Hugoniot curve of a model of nitromethane, where each mesoparticle represents one thousand molecules